(Solution) - a Show by direct substitution in the Schrodinger -(2025 Original AI-Free Solution)

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(a) Show by direct substitution in the Schrodinger equation for the one-dimensional harmonic oscillator that the wave function ?0 (x) = A0e ? a2x2/2, where a2 = mw/h, is a solution with energy corresponding to n = 0 in Eq. (40.22). (b) Find the normalization constant A0. (c) Find the classical turning points and show, in contrast, that the probability density has a maximum at x = 0.